Effect of hydrogen on magnetic properties in MgO studied by first-principles calculations and experiments

We investigated the effects of both intrinsic defects and hydrogen atom impurities on the magnetic properties of MgO samples. MgO in its pure defect-free state is known to be a nonmagnetic semiconductor. We employed density-functional theory and the Heyd–Scuseria–Ernzerhof (HSE) density functional. The calculated formation energy and total magnetic moment indicated that uncharged \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{V}}_{\mathrm{Mg}}^{0}$$\end{document}VMg0 and singly charged \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{V}}_{\mathrm{Mg}}^{-1}$$\end{document}VMg-1 magnesium vacancies are more stable than oxygen vacancies (VO) under O-rich growth conditions and introduce a magnetic moment to MgO. The calculated density of states (DOS) results demonstrated that magnetic moments of VMg result from spin polarization of an unpaired electron of the partially occupied valence band, which is dominated by O 2p orbitals. Based on our calculations, VMg is the origin of magnetism and ferromagnetism in MgO. In contrast, the magnetic moment of the magnetic VMg-MgO crystal is suppressed by hydrogen (H) atoms, and unpaired electrons are donated to the unpaired electronic states of VMg when the defect complex Hi-VMg is formed. This suggests that H causes a reduction in magnetization of the ferromagnetic MgO. We then performed experimental studies to verify the DFT predictions by subjecting the MgO sample to a thermal treatment that creates Mg vacancies in the structure and intentionally doping the MgO sample with hydrogen atoms. We found good agreement between the DFT results and the experimental data. Our findings suggest that the ferromagnetism and diamagnetism of MgO can be controlled by heat treatment and hydrogen doping, which may find applications in magnetic sensing and switching under different environmental conditions.

www.nature.com/scientificreports/ moment that generates a ferromagnetic signal in the material 12,14 . Many studies involving both calculations and experiments indicate that the strength of magnetization results from d 0 ferromagnetism, which is related to the roles of defects and impurities in the system [15][16][17][18][19][20] . Many experiments have shown that the magnetism in MgO is induced by intrinsically charged defects, such as neutral oxygen vacancies and singly and doubly charged magnesium vacancies [11][12][13]17,18 . Kuang et al. used the PBEsol functional with density functional theory to simulate the electronic structure of MgO with vacancies and related it to the magnetic properties of the material 12 .
Additionally, there have been other calculation methods leading to similar results [21][22][23][24] . This research confirmed that Mg vacancies can induce ferromagnetism in the structure. While several theoretical approaches have been used to study intrinsic cation and anion vacancies in MgO, only a few studies have been focused on ubiquitous impurities such as hydrogen. Thus, the characterization of magnetism resulting from defect complexes with different charge states formed by combination of hydrogen impurity atoms and MgO intrinsic defects is still limited. Experiments have revealed that the magnetic moment and ferromagnetism of MgO can be introduced by defect states involving cation vacancies and hydrogen. For example, the formation of oxygen vacancies upon absorption of hydrogen impurities can induce ferromagnetism in MgO nanocrystallites at room temperature 17 . Balcells et al. reported that the reduction of ferromagnetic properties in MgO thin films prepared by radio frequency (RF) magnetron sputtering was related to the hydrogen-driven instability of vacancy centers in the material 24 . By using X-ray absorption spectroscopy (XAS) and Fourier transform infrared spectroscopy (FTIR), our previous work showed that both the ferromagnetism and diamagnetism of MgO at room temperature can be attributed to defects involving magnesium (Mg) vacancies and oxygen-hydrogen (O-H) bonding 20 . Moreover, it was found that suppression of the ferromagnetic properties may be due to formation of O-H bonds via chemical bonding between hydrogen impurities and oxygen in the MgO structure.
Here, we perform first-principles density-functional theory calculations and experiments, such as X-ray diffraction (XRD), vibrating sample magnetometry (VSM) and Fourier transform infrared spectroscopy (FTIR), to gain a deeper understanding of the roles of hydrogen and intrinsic defects in MgO ferromagnetism based on formation of defects studied with first-principles calculation and provide a comparison between these predictions and experiments.

Methods
Computational details. Total energy and electronic structure calculations were performed using the spin polarized DFT approach as implemented in the Vienna ab initio simulation package (VASP) [25][26][27] . The projector augmented-wave method was employed 28,29 . Standard functionals such as the local density approximation (LDA) and the semilocal generalized gradient approximation (GGA) are known to underestimate band gaps and create significant uncertainties in defect energy levels and the electrical activities of defects in semiconductors, especially in wide band gap materials. Instead, hybrid functionals 30 have emerged as a useful alternative for solving problems from underestimated band gaps and energy levels. Therefore, in this work, the exchange-correlation functional was approximated by the Heyd-Scuseria-Ernzerhof hybrid functional (HSE) 31 . For the HSE functional, a Hartree-Fock exchange mixing parameter of 0.25 with the screen parameter of 0.25 were used. The valence electrons of Mg (3s 2 3p 0 ) and O (2s 2 2p 4 ) wavefunctions were expanded in the plane wave basis with a cutoff energy of 500 eV. The calculated band gap of MgO was 6.42 eV, which is in agreement with the experimentally observed value of 6.3 eV 32 . We used a 64-atom supercell with a 2 × 2 × 2 repeating cubic rock-salt MgO primitive cell for defect calculations. The Brillouin zone integration was sampled using a 2 × 2 × 2 k-mesh sampling grid based on the Monkhorst-Pack scheme 33 . Relaxations were performed until the Hellman-Feynman forces acting on each atom were less than 0.01 eV/Å. The calculated lattice parameter of the bulk MgO cubic lattice was 4.199 Å, which is in agreement with our experimental value of 4.22 Å 20 .
To generate defects under different growth conditions, we calculated the formation energy of a point defect X with charge state q defined [34][35][36][37] as where E tot (X q ) represents the total energy of a supercell containing a defect of type X in charge state q, while E tot (bulk) is the energy of a defect-free bulk MgO supercell. n i is the number of atoms from species i (Mg, O, or H) added to a supercell to form the defect cell. μ i is the atomic chemical potential of atomic species i, E VBM is the valence band maximum (VBM) of MgO and E F is the electron Fermi energy. The valence band energy alignment between defect and defect-free supercell approaches was used 38,39 . In Eq. (1), E VBM refers to the valence band maximum (VBM) and represents the electron chemical potential reference. However, the Fermi energy is zero in the DFT calculation, and the absolute value is meaningless for a periodic system. The position of the VBM of a supercell containing a defect is different from that of a defect-free supercell, and this difference depends, in general, on the charge state of the defect. Therefore, a valence band alignment correction is usually applied by matching the two values. The magnitude of this correction is ∆V = < V bulk > − < V defect > , where < V bulk > and < V defect > are the average self-consistent potentials calculated for the bulk and defect supercells, respectively. The alignment correction term (∆V) was approximately 0.1-0.4 eV for our calculations. The chemical potentials μ Mg , μ O , and μ H were limited by the energies of solid Mg, gaseous O 2 , and H 2 , which we referenced as zero energy. To grow MgO in thermal equilibrium, the chemical potential should satisfy µ Mg + µ O = µ MgO . The calculated MgO chemical potential is µ MgO = −6.26eV , which is in agreement with the experimental enthalpy of formation value of − 6.236 eV (− 601.7 kJ/mol) 39 . Therefore, in our calculations, we used µ Mg = −6.26eV − µ O , where − 6.26 ⩽ µ O ⩽0 (note that µ O = 0 was defined as half of the O 2 energy). In the presence of O, Mg forms MgO rather than solid Mg. Therefore, the upper limit of µ Mg is set by MgO precipitation limits, i.e., µ max (1) The structures of all MgO samples were investigated with X-ray diffraction (XRD, Bruker D8 ADVANCE) using Cu-Kα radiation and operated at 40 kV and 40 mA. For Rietveld refinement analyses, high-quality X-ray diffraction patterns were collected in the 2-theta range 10°-120° with an interval step of 0.02° and a scan rate of 2 s/step. Rietveld refinement, using TOPAS software, was utilized to obtain crystallographic information. The FP peak type was utilized as the peak profile for fitting. Note that KCl was inserted into the XRD samples to act as an internal standard. The presence of the hydrogen dopant was characterized by Fourier transform infrared spectrometry (FT-IR, Bruker Tensor 27-Hyperion).

Results and discussion
Defect formation energy and electronic structures. As a first step toward understanding the magnetic properties and effects of hydrogen impurity atoms in MgO, we obtained the electronic structures and formation energies of intrinsic O and Mg vacancy defects as well as H impurity atoms. It was found in previous studies that when the aforementioned defects were present in MgO, they affected the magnetic properties of MgO 17,24,41,42 . Figure 1 shows relaxed atomic structural models for perfect bulk MgO (Fig. 1a) and the hydroxide salt Mg(OH) 2 (Fig. 1b) ), which focuses on nearest neighbor atoms, is also shown in Fig. 1c-f, respectively. The perfect bulk MgO has a rock salt structure with a lattice constant of 4.199 Å, while the hydroxide form Mg(OH) 2 is hexagonal with lattice con-  For the formation energies of native vacancies (Fig. 2), V O is a donor defect with the lowest formation energy at a Fermi energy below 3.5 eV (p-type growth condition), which can be stable with + 2 charges and form with a negative formation energy at Fermi energies below 2.5 eV. V Mg is the lowest formation energy at a Fermi energy above 3.5 eV (n-type growth condition) and forms with a negative value at a Fermi energy above 5 eV. V Mg is a shallow acceptor with a defect transition level change from the charge state q = 0 to the charge state q = − 2 (ɛ(0/− 2)) at a Fermi energy level of 4.7 eV. The relationship between the formation energy of a defect X of charge state q, E f (X q ), and its concentration C(X q ) for a sample under thermal equilibrium is defined as 40 , where N site is the number of equivalent possibilities with the same energies in which the defect can be incorporated (per unit volume), k B is Boltzmann's constant, and T is the temperature. Therefore, the defects with the lowest formation energies are stable and likely to form at high concentrations. These results suggest that V O and V Mg can occur in the Fermi energy range of the sample under O-rich growth www.nature.com/scientificreports/ conditions because both defects can be formed with highly negative formation energies. In addition, the defect concentration can be increased by increasing the temperature (T) of the sample. In general, the shift in Fermi energy due to doping is proportional to the temperature 35 . If a MgO sample is heated at high temperature, the Fermi level will shift to a high energy. Therefore, under heat treatment conditions, V Mg is more likely to form than V O. When hydrogen (H) is doped into the MgO system, among several possible configurations studied for H i , the interstitial structure shown in Fig. 1d turned out to have the lowest energy. The H impurity is likely to occupy interstitial sites close to an oxygen atom and act as a donor defect with + 1 charge and formation energy lower than both V O and V Mg . As a charged defect, it can be compensated by a native defect with the opposite charge. Potential compensating point acceptor defects include V Mg . The formation energy of the H i complex formed with V Mg (H i -V Mg ) was calculated (the atomic structure is shown in Fig. 1e), and H i -V Mg was stable for charge states 0 (H i -V Mg ) 0 and -1 (H i -V Mg ) −1 (Fig. 2). H i +1 can donate an electron to the available states of V Mg charge state 0 ( V 0 Mg ) and -2 ( V −2 Mg ), respectively. H i -V Mg is a shallow acceptor exhibiting a defect transition level change from charge state q = 0 to charge state q = -1 at a Fermi energy level of 4.7 eV with a negative formation energy over the entire Fermi level range. This indicated that H i -V Mg is quite stable and can form at high concentrations. Therefore, V Mg can be a compensating defect in H-doped MgO samples and form H i -V Mg . In the case of V O , hydrogen impurities can form defect complexes with V O by substitution at vacancy sites surrounded by Mg cations (the atomic structure is shown in Fig. 1f). The H O acts as a shallow donor, and it is stable only in charge state + 1 (Fig. 2) ). Therefore, the H in H O behaves as a negative multicenter for defect structures, in agreement with Janotti et al. 43 . However, the formation energy of H O is relatively high and positive throughout the Fermi level range for O-rich conditions. To determine the stabilities of various defect complexes (i.e., Fig. 2), we obtained the defect binding energy, which may be defined To understand the origin of defect-induced magnetization in MgO, we calculated the density of states (DOS) for perfect MgO and Mg(OH) 2 (Fig. 3), as well as for various defect types (Fig. 4). The valence was defined by the state below the Fermi level. According to the orbital-resolved projected DOS, the valence bands of both perfect MgO (Fig. 3a) and Mg(OH) 2 (Fig. 3b)  The total magnetic moments and specific magnetizations of various defect types are summarized in Table 1. The magnetic moment due only to the spin of an electron is 1 Bohr Magneton (µ B ) = 9.27 × 10 -21 emu. To convert this into magnetization, which is the magnetic moment per gram (or the magnetic moment per unit volume), we used the magnetic moment per cubic cell and divided this moment by the cell volume to obtain the magnetization in units of emu/cm 3 . The specific magnetization (emu/g) was obtained by dividing the above magnetization by the MgO density (3.47 g/cm 3 ). Our calculations showed that neutrally charged V 0 Mg and singly charged V −1 Mg and V +1 O were responsible for the magnetic moment of MgO, which originates from the partially occupied valence band. Other defects, i.e., V −2 Mg , V 0 O , and V +2 O , cannot induce magnetic moments in MgO. However, according to the formation energy, binding energy and magnetic moment results, oxygen vacancies can be ruled out under our conditions, as discussed above. In addition, there is V +1 O , which is responsible for the magnetic moment, but V +1 O is not the charge defect with the lowest formation energy. Figure 4a shows the total density of states for neutral V 0 Mg , which creates the hole state in MgO. Spin splitting exists in the valence band, and the spin-down states (gray area) are partially occupied, which is the cause for formation of the magnetic moment of ~ 2 µ B . The projected atomic orbital DOS shows that the maximum valence is dominated by O 2p orbitals (solid violet line), which indicates that the magnetic moment is mainly induced by O 2p orbitals. In the same way, for V −1 Mg (Fig. 4b), spin splitting also occurs in the valence band, and the spin-down states (gray area) are partially occupied; hence, V −1 Mg also creates a magnetic moment (~ 1 µ B ). In comparison, the spin-polarized electron orbitals of V −2 Mg are symmetric. Therefore, V −2 Mg cannot induce a magnetic moment (Fig. 4c). In other words, when removing Mg from MgO, the Mg-O bond is broken to form V 0 Mg or V −1 Mg , which lose two and one donor electrons. This mechanism induced the hole state from O 2p orbitals to compensate for the loss of electrons. However, V 0 Mg has the lowest formation energy and can induce a magnetic moment. Therefore, under our experimental conditions, V 0 Mg is the origin of the magnetism in MgO. When we dope a donor H impurity into perfect MgO (H i ), the H i defect creates unpaired states below the Fermi level and below the valence band (Fig. 4f) with H 1 s orbitals. This doping introduces a magnetic moment of 1μ B (see Fig. 4f) because H i contributes one 1 s electron to the valence band (Fig. 4f) Fig. 4d,e). Based on our calculation results, the origin of the magnetic moment in MgO is largely an unpaired electron from a Mg vacancy, in agreement with other works 12,21-24 . Hydrogen impurities suppress the magnetic moment in magnetic MgO by donating electrons to unpaired electronic states. Therefore, hydrogen is the most significant cause of the reduced magnetic properties in ferromagnetic MgO, which might occur in aged MgO samples 20,24 . For example, magnetic MgO samples are treated in air or under hydrogen gas. In this work, the V Mg in MgO was induced by thermal heating in a vacuum environment because V Mg is easy to form at low energy, whereas H 2 gas injection into the MgO samples at different pressures was used to represent hydrogen doping. The structural and magnetic properties of MgO will be presented and discussed in the Experimental Section.
Experimental results. Figure  To further characterize the XRD results, Rietveld refinements of the data for the 96% MgO commercial sample and the vacuum heated MgO sample were utilized to obtain crystallographic information. Rietveld refinement is a useful method for investigating the full crystal structure details of synthesized materials, e.g., lattice parameters, atomic coordinates, and atomic occupancies. The approach is based on the least squares method, which can be described with the equation: S y = i w i [y i(obs) − y i(calc) ] 2 , where w i = 1/y i , y i(obs) is the observed intensity, y i(calc) is the calculated intensity and S y is the weighted difference between these two values at step i. The refinement procedure involves fitting of the observed XRD pattern to the calculated model structure or crystallographic information file to achieve the minimum S y . The fitting can be evaluated by the weight-profile R-value or R wp , where R wp = i w i y i (obs) − y i (calc) 2 / i w i y i (obs) . The site occupancy factor (SOF) is used to determine the fraction of a site occupied by a specific atom, which can be obtained with the structural factor    www.nature.com/scientificreports/ Figure 6 shows Rietveld refinement plots for the 96% MgO commercial sample and the MgO vacuum heated sample. In this work, the fits between the observed XRD patterns and the structural model showed convergence with good weight-profile R values (%R wp ) and goodness of fit (GOF), as shown in Table 2. The cell parameter a was decreased from 4.2202(2) Å to 4.2163(1) Å upon vacuum heating, which agreed with our DFT relaxed structure. The V Mg results in a decrease in the lattice constant of the cell. The calculated and experimental lattice constants are summarized in Table 3 Tables 2 and  4. The site occupancy factor (SOF) was determined to be 1.0000(56) for Mg in the MgO sample, corresponding to the stoichiometric ratio in the starting material. However, the value was reduced to 0.9623(31) after vacuum heating, which indicated the formation of Mg vacancies. This result corresponded to the formation energy predicted by DFT, and Mg vacancies were induced by vacuum heating and are more stable than oxygen vacancies. Furthermore, equivalent isotropic thermal parameters (Beq.) of Mg and O atoms in MgO 96% commercial   Table 4. These values are useful for describing the motions of atoms in crystal structures, where lighter atoms vibrate stronger and exhibit higher values. Figure 7 shows the magnetization-magnetic field hysteresis curves (M-H hysteresis curves) of commercial MgO powder (black dashed line), vacuum heated MgO (solid blue line), and MgO vacuum heated with H 2 gas at 40 bar (solid green line) and 70 bar (solid red line). Note that all presented data were analyzed with subtraction of the diamagnetic components. After subtraction, we found that the M-H hysteresis curves of all MgO samples showed ferromagnetic behavior with different magnetization values. The 96.0% MgO commercial powder produced an amplitude for the M-H curve with a small magnetization value of approximately 0.31 emu/g, which is close to zero. According to the DFT prediction, bulk MgO is diamagnetic, which should result in a magnetization value of 0 emu/g. In addition, the SOF values for 96.0% MgO commercial powder (Table 4) were equal to 1 for both Mg and O atoms. Therefore, the small magnetism of the commercial powder was from some magnetic element contaminant, and the specification data for commercial MgO powder included 0.0025% Fe and 0.0005% Pb. After heat treatment, the M-H hysteresis curve of the MgO vacuum heated sample increased to give the highest ferromagnetic magnetism of approximately 3.9 emu/g. We propose that the V Mg induced by heat treatment caused the increase in the ferromagnetic magnetism of the MgO vacuum heated sample. Another possible mechanism for inducing magnetism may involve converting H impurities back to their original state (V Mg ) by using heat treatment 20,45 . Next, by doping with hydrogen, we found that the ferromagnetic magnetism of MgO vacuum heated with H 2 gas decreased to approximately 1.63 and 0.31 emu/g for gas pressures of 40 and 70 bars, respectively. Based on our theoretical DFT prediction, Table 1 shows that the neutral V 0 Mg , which was created by vacuum heating, has a total magnetic moment of 2.0478 µ B or 9.75 emu/g, corresponding to a concentration of 3.06% for Mg vacancies (one Mg vacancy in a 64-atom supercell). If we dope hydrogen with the same concentration as V Mg , hydrogen will form a (H i − V Mg ) 0 complex that gives a total magnetic moment of 1µ B or 4.83 emu/g. This prediction corresponds with experiment; when we treated the MgO vacuum heated sample with H 2 gas at 40 bar, the maximum ferromagnetic magnetism dropped from 3.9 to 1.63 emu/g, which was approximately 50% lower than the DFT prediction. Next, if we continued to treat the vacuum heated MgO with a hydrogen concentration greater than the V Mg concentration, the situation might be described as (H i − V Mg ) −1 cases. The magnetization of (H i − V Mg ) −1 will be reduced to zero, consistent with DFT prediction, as shown in Table 1. This is because hydrogen donates an electron to (H i − V Mg ) 0 , which completely fills the unpaired state of (H i − V Mg ) 0 . This results in conversion of the magnetization for the vacuum heated MgO treated with H 2 gas at 70 bar back to the MgO initial value. We showed how introduction of magnesium vacancies V Mg and hydrogen atom impurities can be used to control the magnetic properties of MgO.    Fig. 8a, which shows two strong absorption peaks at 3700 cm −1 and 1500 cm −1 . The absorption peak at 3700 cm −1 corresponds to a -OH stretching vibration in MgO 46 , whereas the absorption peak at 1500 cm −1 is related to bending vibrational modes of physisorbed water 47 . These observations may have resulted from reactions between all MgO samples and humidity in the ambient environment during sample preparation for FTIR measurements. The presence of the -OH vibration is consistent with our calculation and the VSM results, as discussed earlier. The MgO commercial powder (solid black line) showed an absorption peak at  www.nature.com/scientificreports/ 3700 cm −1 , which was higher than that of the vacuum-heated MgO sample (solid green line), as shown in Fig. 8b. This indicated that the MgO commercial powder had already absorbed hydrogen, which might have come from humidity in the ambient environment during sample preparation, as indicated by a very intense physisorbed water peak at 1500 cm −1 . After heat treatment, we found that the vacuum heated MgO sample showed the weakest absorption peak at 1500 cm −1 (see Fig. 8c), implying that the physisorbed water was removed and the structure was changed due to intrinsic defects such as V Mg . After doping the vacuum heated MgO sample with H 2 gas, we observed that the absorption peaks at 3700 cm −1 for MgO vacuum heated with H 2 gas at 40 bar and 70 bar (blue and red solid lines) were substantially increased, which was evidence of hydrogen absorption by the samples (see Fig. 8b). Hydrogen absorption was further confirmed by reheating the sample in a vacuum at 550 °C. The reheated MgO sample doped with H 2 gas at 70 bar (yellow dashed line) showed a decrease in the absorption peak at 3700 cm −1 (see Fig. 8b), indicating that adsorbed hydrogen was eliminated by the heating process.

Conclusion
We used first-principles DFT calculations to investigate formation and the electronic and magnetic properties of MgO samples containing intrinsic vacancy defects and added hydrogen impurity atoms. We found that magnetic moments cannot exist in a perfect MgO crystal or the hydroxide Mg(OH) 2 . Unpaired electrons dominate the formation of magnetic moments in MgO from V Mg , which was confirmed by the formation energy and density of states. Moreover, a hydrogen impurity can be formed as an interstitial (H i ) in MgO and is likely to form a H i − V Mg complex. The magnetic moment of ferromagnetic V Mg -MgO is suppressed by hydrogen in the H i − V Mg form and donated to unpaired electronic states. Therefore, H causes the reduced and degraded magnetic properties in ferromagnetic MgO.
The XRD result showed that new small peaks seen at approximately 35°, 50°, and 60° after heat treatment and hydrogen doping correspond to vacancy defects and hydrogen impurities in the MgO structure. The VSM result confirms that the vacuum-heated MgO sample exhibits the highest ferromagnetic magnetization induced by V Mg . The ferromagnetism of V Mg -MgO can be suppressed by hydrogen doping, as ferromagnetic magnetism is decreased by increased doping with H 2 gas, which results from the formation of H i − V Mg . The presence of doped hydrogen in MgO was confirmed by FTIR measurements. The FTIR result also shows that the hydrogen dopant in MgO can be eliminated by heating. Our findings demonstrate that the ferromagnetic and diamagnetic properties of MgO can be controlled by heat treatment and hydrogen doping, which is useful for applications in magnetic sensing and switching.